kinetics aspects, rheological properties and
TRANSCRIPT
1
Kinetics aspects, rheological properties and
mechanoelectrical effects of hydrogels composed
of polyacrylamide and polystyrene nanoparticles.
Caroline Thévenot, Abdel Khoukh, Stéphanie Reynaud, Jacques Desbrières, Bruno Grassl * Laboratoire de Physico-Chimie des Polymères (L.P.C.P.), UMR CNRS/UPPA 5067, IPREM
FR 2606
Helioparc, 2 Avenue du Président Angot, 64053 Pau cedex 9, France
* Corresponding author ([email protected])
2
ABSTRACT: Snake-cage gels were prepared using monodisperse polystyrene (PS) nano-size
particles (R = 200 nm) in place of the more usually used linear polymer. The kinetics of the
formation of the complementary polyacrylamide (PAM) hydrogel was studied alone or in the
presence of the PS nanoparticles by 1H-NMR. Without PS, the reactivity ratios of the
acrylamide (Am) and the crosslinking agent N,N’-methylene-bisacrylamide (BisAm) were
computed using the initial kinetics of PAM gel at high crosslinker concentration (rA= 0.52, rB
= 5.2, for Am and BisAm respectively). In the presence of PS, during the formation of
nanoparticles composite gels (NPC gels), there was a decrease of the conversion rate with an
increasing fraction of PS nanoparticles. This could be explained by steric effects which induce
an increase of the elastic modulus of the matrix with the increasing fraction of PS
nanoparticles. There was a considerable increase of the rheological properties of the NPC gels
(i.e. tensile modulus) which was more pronounced at higher fractions of nanoparticles. We
used the particular mechanical properties to develop a stimulus responsive (“smart”) material,
i.e. a mechanoelectrical effect which may be used in the development of soft and wet tactile
sensing devices
Keywords: nanoparticles, hydrogel, kinetics, rheological properties, NMR spectroscopy.
3
Introduction
Hydrogels are materials that swell and hold high amounts of water without losing their
shape.1 Polymers and copolymers of acrylamide (Am) are the most commonly used hydrogels
and they have been widely studied. Polyacrylamide (PAM) hydrogels have found applications
in water purification and irrigation,2 in improving soil texture, in pesticide formulations to
limit spray drift 3 and in medical applications.4 They are also used in molecular biology
laboratories as matrices for separating nucleic acid components during DNA sequence
analysis and protein identification.5 PAM hydrogels can absorb relatively high amounts of
water furthermore, their swelling capacity is not very sensitive to pH or electrolytes.6 For
some applications, high water absorption capacity is desired because it increases the
permeability and the biocompatibility of the hydrogels. However, these hydrogels present
poor mechanical properties because water does not contribute to mechanical strength.7 To
increase the range of applications, two types of approaches are necessary: (i) controlling the
microstructure restricting inhomogeneities and (ii) improving the mechanical strength of these
materials while maintaining their water absorption capacity.
To produce hydrogels with relatively high mechanical strength combined with high water
content, some procedures have been reported: (i) “topological (TP) gel”. 8 The TP gels have
figure-of-eight crosslinkers that can slide along the polymer chains. Reflecting this flexible
crosslinker, TP gels absorb large amounts of water, and can be highly stretched without
fracture. (ii) “nanocomposite (NC) gel”. 9 In NC gels, polymer chains can be crosslinked by
inorganic clay slabs on the scale of a several tens of nanometers, instead of organic
crosslinking agents. 10,11 The NC gels are also highly stretchable, and possess other favorable
physical properties such as excellent optical transparency (iii) “interpenetrating polymer
network (IPN)”. 12,13 IPN gels consist of two interpenetrating polymer networks: one is made
of highly crosslinked rigid polymers and the other is made of loosely crosslinked flexible
4
polymers. (iv) “snake-cage (SC) gel”. In SC gels a linear hydrophobic polymer 14 or
polyelectrolyte 15 (snake) with good mechanical properties is entrapped in crosslinked
hydrophilic polymer (cage).
These types of gels with high mechanical strengths have made a breakthrough in finding wide
applications in industrial and biomedical fields, and also raise fundamental problems in gel
science. In our case, we studied particular gels, i.e. PAM hydrogels containing slightly
crosslinked polystyrene (PS) nanoparticules called nanoparticles composite gels (NPC gels),
which belong to the family of snake-cage (SC) gels where monodisperse, hydrophobic and
non-ionic nanoparticles of PS take the place of the linear polymer. We used the particular
mechanical properties to develop a stimulus responsive (“smart”) material, i.e. a
mechanoelectrical effect which may be used in the development of soft and wet tactile
sensing devices
In this work, we studied the polymerization kinetics of these NPC gels by 1H-NMR
spectroscopy and rheological properties. The hydrophobic particles were prepared by direct
(o/w) emulsion polymerization. The free radical polymerization process and the mechanical
properties of these new type of snake-cage gel were compared with those of conventional
hydrogels (i.e., without particles) with similar PAM content and degree of crosslinks (PAM
gels). The difference in their elastic properties was used for producing an electrical potential
by simple compression between two hydrolyzed NPC gels.
5
Experimental section
Materials. For nanoparticles synthesis, styrene (Aldrich) was purified by passing through a
basic activated alumina column before use. Ammonium persulfate [APS, (NH4)2S2O8] and
divinylbenzene were purchased from Aldrich and used as received. Two surfactants were used
for the preparation of nanoparticles: Igepal CO 897© (called NP40, hydrophilic-lypophilic
balance HLB=17.8) obtained from Rhodia© and Ninol© (HLB=11.4) obtained from Stepan©.
Surfactants were used as received. For NPC gels synthesis, acrylamide (Am) (purity >99 %)
and N,N’-methylene-bisacrylamide (BisAm) (purity >99 %) were respectively purchased from
Aldrich and Fluka. 2, 2’-Azobis (2-methylpropionamide)dihydrochloride called
VAZO®56WSP from Dupont Chemicals (Mw = 271.19 g.mol-1, t1/2 = 10 h at 56 °C) was used
as initiator for hydrogel polymerization. Water was distilled three times on Pyrex-quartz glass
apparatus and prefiltered with 0.22 µm Millipore filter just before use to exhibit conductivity
below 0.055 µΩ.cm-1. Reaction mixtures were prepared with the filtered water. All 1H-NMR
spectra were recorded with D2O as solvent (purchased from SDS, purity >99.9 %).
Crosslinked polystyrene latex particles. Latex particles were synthesized according to the
procedure used by Kohut-Svelko et al. 16 The reaction vessel was purged with nitrogen to
remove traces of oxygen. In a typical polymerization, reaction mixture of non ionic
surfactants (NP40 62wt%, Ninol 38wt %) was dissolved in distilled water (200 mL) in a
three-necked round-bottom flask under a nitrogen atmosphere. The purified monomers
styrene (87 g, 0.836 mol) and divinylbenzene (3.7 wt % vs. styrene) used as the crosslinking
agent, were added to the aqueous solution and emulsified under vigorous stirring. This
emulsion was then heated under mechanical stirring up to 70 °C. The aqueous solution of
APS (0.3 g in 5 mL of water) was then added drop by drop. The polymerization was then
allowed to proceed for 24 h at 70 °C under mechanical stirring.
6
Nanoparticles analyses. Nanoparticles were characterized on a dynamic light scattering
apparatus DL 135-45, developed by the IFP (French Petroleum Institute). The technique
works on a very thin suspension layer to avoid multiscattering phenomena and can be
successfully applied to concentrated, dense, and opaque solutions (laser wavelength : 633
nm).The results were confirmed by classical DLS (Sematech) on very diluted latex solutions
(solvent, water; wavelength, 514.5nm). To avoid particles aggregation, solutions were put into
ultrasonic bath during one hour.. Moreover, Environmental Scanning Electron Microscope
(ESEM) analysis (Figure 1), carried out using an ElectroScan instrument operating at 20 kV,
showed that particles are monodisperse. Radius obtained was (200 ± 30) nm from both
techniques
Insert Figure 1
Gel samples. Gels were prepared by classical radical polymerization with BisAm as
crosslinker and VAZO56 as initiator at a temperature reaction of 56 °C, unless otherwise
stated. Reaction mixtures were prepared few hours before polymerization and thoroughly
mixed for 2 h prior to use. The sample solutions were degassed with nitrogen. Hydrogels were
prepared by adding monomer (Am), crosslinker (BisAm), initiator (VAZO®56WSP), in D20
and water for NMR and rheological experiments, respectively. The nanoparticles composite
hydrogels (NPC gels) containing hydrophobic nanoparticles were prepared by addition of PS
latex into the above solution. To prepare different compositions for NPC gels, amounts of
monomer, crosslinker, initiator and PS latex have been varied over a wide range in order to
emphasize their own effect in the polymerization process.
Gels compositions. In this paper, several terms are introduced to classify the hydrogels
compositions: %M refer the total concentration of monomers as a weight percentage; %B, %I
refer respectively to the weight concentrations of crosslinking agent, initiator taking into
7
account both acrylamide and crosslinker; φ represents the volume fraction of polystyrene
particles to the total volume of the reaction mixture, [A] and [B] are the molar concentrations
of vinylic units of acrylamide and BisAm respectively and [I2]0 is the initial molar
concentration of initiator, taking into account the volume of the aqueous phase without the
contribution of hydrophobic PS nanoparticles.
( )% 100 ( )
total mass of monomers gMtotal mass of reaction mixture g
= × (1)
( )% 100 ( )
mass of crosslinking agent gBtotal mass of monomers g
= × (3)
( )% 100 ( )
mass of initiator gItotal mass of monomers g
= × (4)
1H-NMR monitoring. NMR apparatus is a 400 MHz Bruker Advanced AM400
spectrometer. Once the reaction mixtures prepared and mixed, there were poured into NMR
glass tubes (5 mm interior diameter), purged with nitrogen and sealed with paraffin film.
Around 50 measurements were taken continuously during the polymerization in order to
follow the monomers units conversion as a function of time (see Figure 2). Indeed, we
considered three integrations: the first one corresponds to vinylic protons of monomers (at
6.0-6.7 ppm), the second one corresponds to methylene protons of BisAm (4.95 ppm) and the
third one to protons of aliphatic carbon in the polymer backbone to network gathered (at 1.7-
2.7 ppm). Thus, we obtained the overall monomers conversion against time.
Insert Figure 2
Rheological measurements. Rheological measurements of the NPC gels were carried out
using a Bolhin CVOR 150 rheometer equipped with a Peltier device for temperature control.
Parallel-plate geometry was used with a gap of 2 mm. The upper plate was made of stainless
8
with a 40 mm diameter and the lower plate was a stainless Peltier surface. We noticed a
strong adhesion of NPC gel in the stainless surface. Reaction mixture was prepared and mixed
as described above and placed into the parallel plates at a temperature of 56 °C in order to
form the hydrogel in situ. Once the polymerization was complete, dynamic frequency sweep
tests were recorded in an auto-stress mode (equivalent to constant strain mode) at deformation
γ0 = 0.10 maintained constant over the a frequency range of 0.1-10 Hz at 25 °C. For all
experiments, linear regime was checked and a solvent trap containing silicon oil was used to
minimize evaporation. A thin film of oil was applied around the samples (once the gel state
reached) when it was necessary. We compensated for the density and thermal expansions of
the experimental set up by using normal force compensation.
Kinetics aspect of the copolymerization. For propagation in free radical copolymerization, it
is generally considered that the reaction rate for a given comonomer depends only on which
monomer bears the radical at the chain terminus17 . For the molar concentrations of vinylic
units in Am (A) and in BisAm (B) and by considering the equal reactivity of propagating
species whatever the polymerization degree of propagated chains is, this leads to propagation
equations of the form:
* *
[ ] [ ][ ] [ ][ ] AA BAd A k A A k A B
dt− = + (5) * *
[ ] [ ][ ] [ ][ ] BB AB
d B k B B k B Adt
− = + (6)
where A* and B* are the propagating radicals of A and B, respectively; kAA and kBB the rate
constants of homopropagation reactions, kAB and kBA the rate constants of cross-propagation
reactions. The equations rate for propagating radicals A* and B*, are:
9
** * * * *
2 [ ] 2 [ ] [ ][ ] [ ][ ] [ ]² - [ ] [ ] d AB BA AA AB
d A F k I k B A k A B kt A kt A Bdt
= − + − (7)
** * * * *
2 [ ] 2 [ ] - [ ][ ] [ ][ ] - [ ]² - [ ] [ ] d BA AB BB AB
d B F k I k A B k B A kt B kt A Bdt
= + (8)
where 2Fkd[I2] means the formation rate of active centers I* issued from the chemical
decomposition of the initiator I2, F the efficiency parameter of initiator, ktAA[A*]2 and
ktBB[B*]2 the rates of homotermination reactions and ktAB[A*][B*] the rate of cross-
termination reactions. The quasi steady-state approximation applied to radicals assumes that
the variation of [A*] and [B*] is negligible towards the other reaction rates, thus d[A*]/dt =
d[B*]/dt = 0. In terms of the creation and loss of propagating radicals, the contribution of
initiation and termination reactions is negligible compared to that of the cross-propagations,
thus:
* * * * * *2 2 [ ] [ ]² - [ ] [ ] [ ]² - [ ] [ ] d AA AB BB ABF k I kt A kt A B kt B kt A B= = (9)
[ ][ ]
0.5*
*tAABA
AB tBB
A A kkk B kB
⎡ ⎤ ⎛ ⎞⎣ ⎦ = = ⎜ ⎟⎡ ⎤ ⎝ ⎠⎣ ⎦ (10)
The instantaneous composition of copolymer was determined using the Mayo-Lewis 18
copolymer equation given below:
[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]
A
B
d A A r A Bd B B A r B
⎛ ⎞ ⎛ ⎞+= ⎜ ⎟ ⎜ ⎟+⎝ ⎠ ⎝ ⎠
(11)
where the reactivity ratios rA and rB are defined as following:
AAA
AB
krk
= ; BBB
BA
krk
= (12)
The instantaneous mol fraction of [A] incorporated, FA, is given by:
10
[ ] ² (1 - )
[ ] ² 2 (1 - ) (1 - )² A A A A
AA A A A B A
d A r f f fFd A B r f f f r f
+= =
+ + + (13)
where fA and fB are the mol fractions of monomers A and B, respectively. FB is obtained by
interchanging the subscripts A and B. These expressions form the basis for finding
composition and sequence length distributions.
[ ] [ ] [ ]
AAf
A B=
+ ;
[ ] [ ] [ ]
BBf
A B=
+ (14)
If the composition drift and initiator decomposition rate are slow, the concentrations of A*
and B* can be assumed almost constant throughout the reaction, so that [A] and [B], at least
at early values of conversion, will yield first-order decay kinetics of the form:
-0[ ] [ ] A tA A eα= ; -
0[ ] [ ] B tB B eα= (15 and 16)
where αA and αB are the apparent rate constants of propagation reactions of A and B
respectively, with
* * [ ] [ ] A AA BAk A k Bα = + ; * *
[ ] [ ] B BB ABk B k Aα = + (17)
Otherwise, the reactivity ratios can be determined by finding the ratio of these rate constants,
determined over early conversion, for separate experiments in which the relative initial
concentrations [A]0 and [B]0 varied. Using equations 9, 10 and 12 that yields
0
0
0
0
[ ]1 [ ] [ ]
[ ]
AA
BB
ArB
A rB
αα
+=
+ (18)
11
Results and Discussion
1. Kinetics aspect by 1H NMR
1.1 PAM gels at low crosslinker concentration
Insert Table 1
Figure 2 shows raw spectra for a typical 1H-NMR monitoring experiment (run A3 in Table 1).
The signal at 4.7 ppm corresponds of the residual water in D20. The signal decrease between
6.0 and 6.7 ppm and the signal increase between 1.7 and 2.7 ppm show the conversion of
vinylic units A and B, whereas the signal decrease at 4.95 ppm is due chiefly to the
conversion of the crosslinking agent, i.e. it corresponds to one vinylic function of BisAm.
These three signals yield the monomers conversion, according to the following equations:
pA = 1-[A]/[A]0 (19)
pB = 1-[B]/[B]0 (20)
The first series of experiments (series A in Table 1), were prepared with different amounts of
initiator while the fraction of crosslinking agent %B was kept roughly constant.
Unfortunately, the concentration of B was too small to make the signal at 4.95 ppm accurate.
Figure 3 shows only monomer conversion pA versus time for different initiator concentrations
while keeping %B and %M constant.
Insert Figure 3
The curves in Figure 3 can be treated approximately as first order over a significant portion of
the reaction. Nevertheless, fits of the form:
pA = 1 - exp (-αA . t) (21)
12
are also shown in Figure 3, where αA is the first-order decay rate constant defined by equation
15. The fit is best for all the reactions presented in Table 1. The ln[A] versus time curves did
not show a steepening with increasing conversion. This indicates that auto acceleration was
absent or insignificant. The inset in Figure 3 shows αA vs [I2]00.5 corresponding to equation 17
with [B*] << [A*] and plotted for runs A1 to A4. The linearity is quite good for all values.
The slope of the plot is hence related to the apparent rate constants kapp via
dαA/d[I2]00.5 = kapp = 1.09 × 10-1 s-1.mol-1/2.L1/2
for %B = 1 and where the approximation is made that the initiator decay rate is slow
compared to the time for the complete reaction, so that [I2] ≈ [I2]0. As expected, the reaction
time is short compared to the half-time life of initiator (10 h at 56 °C). Our system using azoic
initiator is significantly faster than the classical one using a persulfate initiator for the free
radical homopolymerization of Am: kapp = 1.05 × 10-2 s-1.mol-1/2.L1/2 and 4.58 × 10-3 s-1.mol-
1/2.L1/2 at 50 and 60 °C respectively. 19 These values favor the formation of the NPC gel in
reasonable time with %B = 1, a small amount of initiator and a conversion close to 100%.
The series of experiments concerning the same reaction mixture at different temperatures (cf.
Table 1, Runs B1 to B4) is plotted on the Figure 4. The inset shows a linear variation of
ln(αA) versus 1/T (T in Kelvin) according to the Arrhenius relation
αA = αA0 . exp (-∆E / RT) (22)
where ∆E is the apparent activation energy of the global process in this free radical
copolymerization of acrylamide and R the perfect gas constant. The data from the inset Figure
4 yield activation energy ∆E = 67 kJ.mol-1 as the same order of classical radical
polymerization. 19
Insert figure 4
13
1.3. PAM gels at high crosslinker concentration
A series was prepared with high concentrations of crosslinker (runs C5 to C11 with %B
varying from 5 to 27) to determine the influence of a great increase of the amount of vinylic
unit. Indeed, if [B] is high enough, the signal at 4.95 ppm is accurate. So, kinetics study can
be performed with both considering the conversion of the two monomers (pA and pB) and
determining αA and αB.
Figure 5 shows the initial decay rates, i.e. the initial slope of semi-logarithmic plot of
monomer concentration ((1- pA) and (1- pB)) versus time for runs C7 and C11. The monomer
decay in each case follows a first-order kinetics over almost the entire range of the
experiments, as shown in Figure 6. Steady state approximations and slow monomer
concentration ratios variation fit well. Inset of Figure 6 shows the determination of rA and rB
using the ratio of A and B rate constants from equation 18 (runs C5 to C9). The experimental
values of rA and rB are 0.52 ± 0.04 and 5.2 ± 0.8, respectively. Even in the case of high drift,
the initial decay rates should still yield a good approximation for the reactivity ratios. This
method, using rate constants, issued from NMR data is convenient and accurate provided that
the same initiator concentration is used in each experiment.
Nevertheless, from equation (18), it can be seen that the value of rB is dependent on low value
of the ratio [A]0 / [B]0 where there is little variation in αA / αB . The main conclusion is the
very high reactivity of BisAm compared with Am, as already reported elsewhere (rA = 0.57
and rB = 3.4 at 22 °C 20). As we can observe in Figure 6, in the first 1000s of the
copolymerization, the major part of BisAm was consumed while the Am monomer
conversion reached only 0.86. This phenomenon was enhanced by increasing [B]0.
Insert figure 5 and 6
14
Moreover, the use of the Mayo-Lewis theory allows computing the sequence length
distribution. WBB denotes the probability that B* adds to B. Using the reactivity ratios, this
can be expressed, at any conversion point p, during the reaction as
( )( )( )( 1) 1
B BBB
B B
r f pW pf p r
=− +
(23)
Where conversion point p is the total conversion of monomers.
The probability of having a sequence of k monomers B in a row , followed by a monomer A,
PB,k, then follows the well-known geometric distribution : 17
1, )(1 ) k
B k BB BBp W W −= − (24)
pB,k(p) from measurements at each point p is hence the instantaneous sequence length
distribution. The moments of this distribution are well-known. The instantaneous number-
average sequence length of monomer B, <NB>n, at conversion point p, is
1( )1 ( )B n
BB
N pW p
=−
(25)
To obtain the appropriate expressions for monomer A, the subscript A is substituted for B in
each variable in the above equations.
Figure 7 shows the probability that B* adds to B and the instantaneous number B sequence
lengths, <NB>n vs. conversion, for experiment C6. These values were computed from eqs. 23-
25, using the value of rB = 5.2.
Insert figure 7
Figure 8 shows a mechanism of the network formation, by taking into account the very strong
difference between rA and rB (rA = 0.52 ± 0.04 and rB = 5.2 ± 0.8 in our system). Run C6 was
chosen in order to demonstrate the occurring phenomena. Before polymerization begins, there
is a small part of crosslinker molecules in the reaction mixture with high concentration of
15
vinyl groups. Then, free radical polymerization begins with a few chains of linear PAM
growing incorporating some BisAm molecules. Indeed, with [B] = 55.10-3 mol-1.L-1, an
average quantity of one BisAm molecule against 9 Am molecules are polymerized (FB =
0.11). Moreover, the determination of <NB>n (at p=0, <NB>n = 1.3) can be understood as an
average of the incorporation in the PAM growing chain of a sequence of two BisAms at one
point followed further by two individual BisAms (4/3 ≈ 1.3). In consequence (Figure 8a), the
sequence of two BisAms would be the cause of the initial formation of very dense and
crosslinked microdomains. However, the incorporation of only one BisAm permits the
formation of simple node. Finally (Figure 8b), these phenomena, occurring during the early
stages of the polymerization, lead to a network which already exhibits structural
inhomogeneities.
Insert figure 8
Other factors than the reactivity ratios have been studied to explain these inhomogeneities
such as the nature of the crosslinker, 21 the nature of the solvent22 and the temperature. 23
Finally, our results confirm the commonly held view of the existence of microdomains of
highly crosslinked and reticulated clusters, joined by PAM chains. 22,24,25
Thus, using NMR technique for studying polymer networks is very interesting because a
mechanism of the network formation can be built thanks to the determination of some kinetics
constants; in consequence, the microstructure of PAM gels can be controlled by restricting
inhomogeneities. Indeed, small amount of B with %M = 7 permits limiting high crosslinked
microdomains and inhomogeneities. That is why these concentrations (or less) will be used
for the following kinetics study of NPC gels. After the kinetics study of PAM gels, the
formation of NPC gels and their mechanical strength were studied in the aim of widest future
applications.
16
1.4 Nanoparticle composite gel (NPC)
In this part, the influence of the introduction of latex PS nanoparticles in the reaction mixture
was analyzed in terms of apparent rate constants of propagation reactions of A with a low
concentration of B (Table 2).
Insert Table 2 - Insert Figure 9
For experiments D1 to D5, the incorporation of latex particles showed a decrease of αa along
with an increase of the nanoparticles volume fraction, φ. Although αa is lower, the final
conversion of PA for D5 and D6 experiments can reach up to 0.8 but the polymerization rate is
slower and the time to have the same conversion is higher than for the PAM matrix alone
(about 4000s). This result was unexpected: indeed, the nanoparticles which are just
incorporated in the PAM matrix are neutral in terms of reactivity and were not supposed to
influence the kinetics of the crosslinked PAM. This feature occurred without any modification
of the first-order kinetic plot, as shown in Figure 9. As shown in the following section, the
incorporation of latex particles increased the elastic modulus of the gel, and could explain the
slower propagation rate. However, comparison of runs D5 and D6 performed with and
without crosslinker exhibited the same rate constants (values of αA for D5 and D6 are
respectively equal to 0.37 × 10-3 and 0.38 × 10-3 mol.s-1.L-1) proves that gel effect does not
occur in our system. Moreover, the presence of surfactants in the reaction medium could act
as an inhibitor by chain transfer, since propagating radicals will be removed and very few new
ones will be created. In this case, chain transfer agent actually seemed to lead to a decrease of
the conversion rate. This was explained by runs D7 and D8, with no PS particles and different
overall concentration of surfactants mixture used for PS nanoparticles (D7: Ninol = 0.48 wt%
and NP40 = 1.18 wt%, and D8: Ninol = 0.26 wt% and NP40 = 0.59 wt %). The results were
compared to those obtained for the experiment D9 containing no surfactant and showed no or
very few contribution of the surfactants in the kinetic process of PAM gel formation.
17
The decrease in conversion rate along with the fraction of PS particles cannot be explained by
gel effect or by the presence of residual surfactant. Instead, we think that this feature is rather
due to a steric effect. Indeed, the latex particles are spherical objects; we can assume that they
adopt a regular space organization of cubic lattice in the gel. Several types of cubic lattices
could be considered, for example a simple cubic (sc), a body-centered cubic (bcc), or a face-
centered cubic (fcc) structures. The lattice constant, ai, is related to the distance between the
planes, dhkl , through the equations : asc = d100, abcc = 21/2d100, and afcc = 31/2d100. Considering
that ai3 is the cubic lattice volume and that there are 1, 2, and 4 scattering objects per lattice
for the sc, bcc, and fcc, respectively, it is then possible to write that the lattice constant ai is a
function of the radius R and of the particles volume fraction φ :
( )33
4 3 Ra
α π
φ= (26)
Where α is the prefactor depending of the nature of the cubic lattices, 1, 2 and 4 for sc, bcc,
and fcc, respectively. In the case where R = 202 nm and φ = 0.13, the edge to egde distance d
between surface particles are 239, 481 and 169 nm for simple cubic (sc), a body-centered
cubic (bcc), or a face-centered cubic (fcc) structure respectively. Moreover, the radical
polymerisation of Am with no crosslinker (at 56°C and with the same initiator concentration
as in run A3) provided a linear PAM chains with high molecular weight (Mw = 1.35 × 106
g.mol-1) and a radius of gyration of 82 nm. The corresponding diameters are of the same order
of magnitude as the distance d between surface particles. In this case, the particles could be
considered as a hindrance of the growing chain and slow down the propagation rate of the
growing chain in the reaction medium. In fact, the rate of propagation αA decreased by a
factor close to ten between run D9 containing no particle and runs D5 and D6 realized with
13% of PS particles, with and without crosslinker, respectively. It is clear that if we take into
18
account these geometric considerations, the decrease in conversion rate with the fraction of
PS particle could surely be explained by a steric effect.
In addition, even if this spectroscopy technique is widely used for monitoring kinetics on
linear polymers, our study shows that it is also easily possible in the specific case of three
dimensional polymers containing additional particles or not. In our knowledge, this specific
case was not yet developed in literature.
2. Rheological behavior
Thanks to the kinetics aspects described above, we ensured that NPC gels syntheses occur in
classical ways and reach to completion. So, we wanted to study the rheological properties of
these NPC gels. As previously shown, PS latex nanoparticles were considered as well-known
model nanoparticles which can be easily used in our hydrogels systems. The influence of PS
nanoparticles on rheological behavior of NPC gels was studied in the same experimental
conditions as for kinetics study with a volume fraction of nanoparticles φ ranged from 0 to
26%. The samples composition is given in Table 3 (runs G1 to G6).
Insert Table 3
Once the polymerization was achieved, dynamic oscillatory tests in frequency were
performed between 0.1 and 10 s-1. The good reproducibility of the results of G'(w) confirmed
that the polymerization has reached completion. For all hydrogels, G'(w) stayed constant with
a standard deviation close to 0.5%, and G’’(w) could be considered negligible against G'(w).
The stability and the relative large value of G'(w) compared to G''(w) over a range of at least
three frequency decades is a classical characteristic feature of a crosslinked hydrogel.7,26 This
stability also indicated that the permanent chemical crosslinks were not destroyed by the
increasing frequency at constant strain γ0. Moreover, γ0 = 0.10 was within the linearity
19
domain. Indeed, G' was measured as a function of increasing strain amplitude γ0. G' remained
constant for low strains (γ0 < 0.35). The linearity domain decreased as the elasticity of the
hydrogel increased.
Experimental data are reported in Table 3 and Figure 10 shows the variation of G’ with the
volume fraction, φ of PS nanoparticles. The experimental results showed a strong
reinforcement of rheological properties of NPC gels which was greater at higher nanoparticles
content.
In order to evaluate in a better way our NPC gels, we used a rheological behaviour modelling
of a composite of two elastic bodies without interfacial tension, proposed by Kerner 27 and
revisited by Bousmina 28. The elastic modulus of the blend Gb can be related to the elastic
modulus of the matrix Gm and the dispersed phase Gd as follows:
(2 3 ) 3 ( - ) (2 3 ) - 2 ( - )
d m d mb m
d m d m
G G G GG GG G G G
φφ
⎛ ⎞+ += ⎜ ⎟+⎝ ⎠
(27)
We can consider that Gd is close to 6.109 Pa 29 and the elastic modulus of the matrix Gm =
2150 Pa as measured for the hydrogel without PS nanoparticles (run G1). Thus, a theoretical
behavior was plotted and reported in Figure 10 along with our experimental data. It is obvious
that our NPC gel systems do not follow the Kerner model i.e. that elastic modulus of the
blend Gb obtained are higher than the expected ones for volume fractions higher than 0.05.
This difference could be explained with the elastic modulus Gm values. Indeed, when
nanoparticles are incorporated into the gel, the kinetics of NPC gels is greatly dependent on
the nanoparticles content (see kinetics section) and the rheological properties may be affected
by the modifications of the gelation process. Such, Gm drastically increased as the volume
fraction of nanoparticles contained in our NPC gels. Thus, Gm obtained from eq. 27 shows
20
this phenomenon: 7476 and 19 219 Pa for G4 and G6 respectively. Otherwise, a slight
adhesive interaction between PS nanoparticles and PAM matrix can explain the difference
between experimental and theoretical data.
Insert Figure 10
3. Mechanoelectrical effects of hydrolysed NPC gels
Hydrogels with high mechanical strength may have several applications and among them, we
chose to evaluate the chemoelectrical properties of our systems.
It is well known that polyelectrolyte gels can contract or deform under an electrical stimulus,
that is, a gel can convert the electrical energy into mechanical work. The reverse process was
also previously reported, 30 it produces electrical potential from mechanical deformation. As
shown in Figure 11a, a cell containing two stacked layers of hydrolysed NPC was made: the
bottom layer was a gel containing 26% of nanoparticles and the top one did not contain any
particles. Indeed, the bottom part which presents interesting rheological properties shows also
a different behaviour under compression (the deformation of this bottom layer is lower than
the one of the top layerif the same stress is applied). A pair of platinum wire electrodes, one
as reference and the other one as working electrode, was inserted to measure the electrical
potential. When the top gel layer was compressed (with a ∆L1/L deformation), the extra
protons migrated to the bottom gel layer, slightly deformed (∆L2/L), through the interface
until the Donnan equilibrium was reached. An electrical potential variation was observed
during this period as shown in Figure 11b. These preliminary results showed that the tactile
sensing systems were successfully made from polymer gel. Moreover, the electrical signal
enhanced in proportion to the amplitude of the applied strain ∆L/L (or stress).
21
On the basis of this principle, a soft and wet tactile sensing device could be developed by
connecting the electrodes to two NPC gel layers exhibiting different elastic modulus, as
previously shown.
Insert Figure 11
On the basis of swelling and contraction of a weak polyelectrolyte gel, Katchalsky et al. 31
proposed a so-called ‘‘muscle’’ model which was referred to a chemomechanical system.
Thanks to this similarity and the common feature with the natural tissue (softness, wetness,
elasticity, and some other rheological specified characteristics), the soft mechanoelectrical
system obtained from a NPC gel may open new possibilities in the investigation of artificial
tissue-like tactile perception for robotics or psycho sensorial material area.
Conclusion
We studied particular gels which belong to the family of snake-cage gels where
monodisperse, hydrophobic and non ionic nanoparticles take the place of the linear polymer.
The polymerization kinetics of PAM hydrogel with and without polystyrene nanoparticles
(NPC gels) has been performed by 1H-NMR spectroscopy. Reactivity ratios were computed
using initial kinetics in the case of PAM gels at high crosslinker concentration. Furthermore,
it is possible to determine the instantaneous and cumulative sequence length distribution and
average, based on the Mayo-Lewis model. The different results and their interpretation are in
accordance with previous studies on inhomogeneities in this kind of hydrogel.
For the NPC gels, the decrease of conversion rate with the PS nanoparticles content could be
explained by a steric effect which probably induces an increase of the elastic modulus of the
matrix and is related to nanoparticles content. The results show a strong reinforcement of
mechanical properties of NPC gels which is more pronounced for the higher fraction of
nanoparticles. These differences of rheological properties have been used for producing an
22
electrical potential by simple compression between two hydrolyzed NPC gel layers. This
concept can be used to develop a soft and wet tactile sensitive device. The soft
mechanoelectrical system made with a NPC gel may open new possibilities in the
investigation of artificial tissue-like tactile perception for robotics or psycho sensorial
material area, for example.
Acknowledgment
The authors wish to thank Nicolas Kohut-Svelko for his help in the preparation of PS latexes,
Gérald Clisson and Francis Ehrenfeld for technical assistance. The Communauté
d’Agglomération de Pau (France) is greatly thanked for financial support. The authors would
like to acknowledge Virginie Pellerin for ESEM images, Roger C. Hiorns for help in the
preparation of the manuscript and Jeanne François for initiating this work.
23
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25
Captions of Tables and Figures
Table 1. Experimental conditions and kinetics parameters for the hydrogel polymerization Table 2. Experimental conditions and kinetics parameters for the NPC hydrogel polymerization Table 3. Experimental conditions and rheological results for the NPC hydrogel polymerization Figure 1. ESEM images of PS latex particles Figure 2. Spectra evolution of reaction mixture for the in situ PAM hydrogel formation in 1H-NMR probe Figure 3. Am conversion pA as a function of t, at T =56°C, including the first-order fit according to eq 15. Reaction designations are from Table 1. Inset: First-order monomer decay rates vs. [I2]0
1/2 for %B = 1 Figure 4. Am conversion pA as a function of t, at various temperatures T, including the first-order fit according to eq 15. Reaction designations are from Table 1. Inset: first-order monomer decay rates in function of 1/T Figure 5. Initial decay rates of monomers A and B; 1-pA (full symbols) and 1-pB (empty symbols) versus time for runs 7 and 11
Figure 6. Am (pA) and BisAm (pB) conversion as a function of t, at %B = 9.3 and T =56°C (run C10), including the first-order fit according to eq 15 and 16. Inset: determination of rA and rB using the ratio of A and B rate constants from eq 18. The values of rA and rB are 0.52 and 5.2, respectively
Figure 7. Wbb ( ) and <NB>n ( ) versus total monomers conversion p for Run C6 Figure 8. Mechanism of free-radical copolymerization in network formation
Figure 9. Am conversion pA as a function of t, in the presence of PS nanoparticles at T = 56°C, including the first-order fit according to eq. 15. Reaction designations are from Table 2 Figure 10. Evolution of elastic modulus as a function of the volume fraction of PS nanoparticles incorporated into the NPC gel. The line represents the Kerner’s model and the points are experimental data
Figure 11. Time profile of tension (∆V) (b) produced by compression of two hydrolyzed NPC gels (a): gel 1 without particles and deformation of ∆L1/L and gel 2 with 26% of PS nanoparticles with a deformation of ∆L2/L (L = L1,0 + L2,0; ∆L1= L1,0 - L1 and ∆L2= L2,0 - L2)
26
Table 1: Experimental conditions and kinetics parameters for the hydrogel
polymerization
Run T
(°C) %M
[A]
(× 101)
(mol.L-1)
%B
[B]
(× 103)
(mol.L-1)
%I
[I2]0
(× 103)
(mol.L-1)
αA
(× 103)
(s-1)
αB
(× 103)
(s-1)
A1 56 7.1 9.8 1.0 9.2 0.13 0.33 2.94 __
A2 56 7.1 9.9 1.1 9.7 0.41 1.07 4.20 __
A3 56 7.1 9.9 1.1 9.7 0.98 2.55 6.01 __
A4 56 7.8 10.8 0.9 9.4 2.00 5.72 7.34 __
B1 36 7.1 9.8 1.0 9.0 1.0 2.58 0.62 __
B2 46 7.1 9.8 1.0 9.0 1.0 2.58 1.80 __
B3 50 7.1 9.8 1.0 9.0 1.0 2.58 2.15 __
B4 56 7.1 9.8 1.0 9.0 1.0 2.58 6.17 __
C5 56 7.6 10 4.7 46 0.046 0.13 2.08 4.05
C6 56 7.5 10 5.6 55 0.047 0.13 1.87 4.26
C7 56 7.6 9.9 6.6 65 0.046 0.13 2.08 4.45
C8 56 7.6 9.9 7.5 74 0.046 0.13 2.15 4.44
C9 56 7.7 9.9 8.2 82 0.046 0.13 1.46 3.67
C10 56 7.8 9.9 9.3 94 0.091 0.26 1.94 4.54
C11 56 5.1 5.2 27 178 0.29 0.54 1.52 4.88
27
Table 2. Experimental conditions and kinetics parameters for the NPC hydrogel polymerization
Run T
(°C) %M
[A]
(× 101)
(mol.L-1)
%B %I
[I2]0
(× 103)
(mol.L-1)
φ (%)
αA
(× 103)
(s-1)
D1 56 7.1 9.9 1.1 0.98 2.55 0 no surfactant 6.01
D2 56 7.2 10 1.0 0.97 2.57 0.31 4.37
D3 56 7.0 9.7 1.0 1.06 2.72 0.72 3.41
D4 56 7.2 10 1.0 1.05 2.77 1.83 3.39
D5 56 4.3 6.0 1.0 0.99 1.56 12.6 0.37
D6 56 4.2 6.0 0 1.16 1.81 13.1 0.38
D7 56 4.5 6.2 1.0 1.00 1.66 0 with surfactantsa 3.58
D8 56 4.5 6.2 1.2 1.25 2.08 0 with surfactantsb 3.74
D9 56 4.4 6.1 1.1 0.98 1.54 0 no surfactant 3.17
a : ninol = 0.48 wt% ; NP40 = 1.18 wt% b: ninol = 0.26 wt% ; NP40 = 0.59 wt%
28
Table 3. Experimental conditions and rheological results for the NPC hydrogel polymerization
Run %M
[A]
(× 101)
(mol.L-1)
%B
[B]
(× 103)
(mol.L-1)
[I2]0
(× 103)
(mol.L-1)
φ (%) G’ (Pa)
G1 7.1 9.9 1.0 9.2 2.6 0 2 200
G2 7.1 9.9 0.9 8.1 2.8 0.32 2 300
G3 7.1 9.9 0.8 7.0 2.8 1.81 2 100
G4 7.0 9.8 0.8 7.1 3.5 15.1 10 800
G5 7.3 10.2 0.8 7.1 3.4 20.3 19 000
G6 7.4 10.3 0.8 7.2 3.4 26.0 36 100
29
Figure 1. ESEM images of PS latex particles
30
Figure 2. Spectra evolution of reaction mixture for the in situ PAM hydrogel formation in 1H-NMR probe
t = 3480 s
t = 3120 s
t = 3240 s
t = 3300 s
t = 0 s
t = 3360 s
t = 3660 s
t = 3900 s
t = 4680 s
t = 5100 s
t = 5220 s
31
Figure 3. Am conversion pA as a function of t, at T =56°C, including the first-order fit according to eq 15. Reaction designations are from Table 1. Inset: First-order monomer decay rates vs. [I2]0
1/2 for %B = 1
32
Figure 4. Am conversion pA as a function of t, at various temperatures T, including the first-order fit according to eq 15. Reaction designations are from Table 1. Inset: first-order monomer decay rates in function of 1/T
33
Figure 5. Initial decay rates of monomers A and B; 1-pA (full symbols) and 1-pB (empty symbols) versus time for runs 7 and 11
34
Figure 6. Am (pA) and BisAm (pB) conversion as a function of t, at %B = 9.3 and T =56°C (run C10), including the first-order fit according to eq 15 and 16. Inset: determination of rA and rB using the ratio of A and B rate constants from eq 18. The values of rA and rB are 0.52 and 5.2, respectively
35
Figure 7. Wbb ( ) and <NB>n ( ) versus total monomers conversion p for Run C6
36
Figure 8. Mechanism of free-radical copolymerization in network formation
covalent crosslinking growing radical chainAm BisAm
will form a high density crosslinkage
will form a simple node
(a) (b)
high crosslinking concentration
37
Figure 9. Am conversion pA as a function of t, in the presence of PS nanoparticles at T = 56°C, including the first-order fit according to eq. 15. Reaction designations are from Table 2
38
Figure 10. Evolution of elastic modulus as a function of the volume fraction of PS nanoparticles incorporated into the NPC gel. The line represents the Kerner’s model and the points are experimental data
39
Figure 11. Time profile of tension (∆V) (b) produced by compression of two hydrolyzed NPC gels (a): gel 1 without particles and deformation of ∆L1/L and gel 2 with 26% of PS nanoparticles with a deformation of ∆L2/L (L = L1,0 + L2,0; ∆L1= L1,0 - L1 and ∆L2= L2,0 - L2)
a
∆L
L2,0
L1 L1,0
1
2
L
mV + ∆V
1
2
mV
2
b ∆L2/L
∆L1/L